The invention is based on a measuring device for measuring the mass of a flowing medium, or flow rate meter, a defined herein. In a known flow rate meter (SAE Paper No. 880,560), there is a danger that the ceramic substrate, of only a few tenths of a millimeter thick, having the at least one temperature-dependent resistor film will be destroyed by improper handling of the body of the flow rate meter. This may happen for example if it is dropped from a height of over about 60 cm, or from intermittent impacts, or if some object, or a person's fingers, unintentionally touch the ceramic substrate directly.